Problem 1: Consider the vector space R³. Let {e1, e2, e3} be the standard basis of R³. Find a basis B of R³ for which [e1] B = [e2]B = 2 and [e3] B = 1
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- What is The NPV for Machine B=Please show all work ง 5. Evaluate the vector surface integral JJ (+2², x + 2y + 32², 5x − 2y + 2³) . Ndo. S Here, S is the sphere Sy²+2 1. = Since S is a closed surface, the outside of S is considered as the positive side on S. Hint: use the divergence theorem.Evaluate the integral. Check your answer by differentiating. (Remember the constant of integration.) (x4 − 9x2 + 2) dx
- Let f(x) = √√x, g(x) = x + 8 and h(x) = 5. (f + g)(16) X Compute the following function value.Which of the graphs below is the correct graph of y=-tan(x)? Graph A 1 0 -1 -2 Graph B -1 -2 1 0 Graph C Graph D A Graph A B Graph B C Graph D -1 -2 1 0Find at least the first four nonzero terms in a power series expansion about x = 0 for a general solution to the given differential equation. y'' +(x+6)y'+y=0 y(x) = ☐ + ... (Type an expression in terms of a and a₁ that includes all terms up to order 3.)